Mathematics 2016 Objective — Question 1
Algebra 1. 4² + |4| + |-4| - 4² = ?
- A. 4+C3:L12A1C3:L32
- B. 0
- C. 4
- D. 8Correct
Explanation
4²+|4|+|-4|-4² = 16+4+4-16 = 8 (any negative value inside modulus becomes positive).
Post-UTME Mathematics 2016 Objective Past Questions
All 60 questions from the Post-UTME Screening (Post-UTME) Mathematics 2016 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Mathematics 2016 Objective — Question 2
Algebra 2. 3⁵/3³ = ?
- A. 1
- B. 3
- C. 9Correct
- D. 27
Explanation
3⁵/3³ = 3^(5-3) = 3² = 9.
Mathematics 2016 Objective — Question 3
Algebra 3. 3² x 3³ x 1/3⁴ = ?
- A. 1
- B. 3Correct
- C. 9
- D. 27
Explanation
3²x3³x3⁻⁴ = 3^(2+3-4) = 3¹ = 3.
Mathematics 2016 Objective — Question 4
Algebra 4. ∛√64 = ?
- A. √2
- B. 2Correct
- D. 8
Explanation
∛√64 = 64^(1/6) = (2⁶)^(1/6) = 2.
Mathematics 2016 Objective — Question 5
Algebra 5. What is the value of x in the equation x/2 + x/3 = 10
- A. 12Correct
- B. 14
- D. 18
Explanation
LCD is 6: 3x+2x=60, 5x=60, x=12.
Mathematics 2016 Objective — Question 6
Algebra 6. What is the solution interval of the inequality 6x-2 ≥ 3x+10
- A. (∞,4)
- B. (-∞,4)
- C. (-4,∞)
- D. [4,∞)Correct
Explanation
6x-3x ≥ 10+2, 3x ≥ 12, x ≥ 4, giving the interval [4,∞).
Mathematics 2016 Objective — Question 7
Algebra 7. What is the value of x in the equation (4/3)√(10x-4) - 8 = 0
- A. 0
- B. 2
- C. 4Correct
- D. 6
Explanation
√(10x-4) = 6, so 10x-4=36, 10x=40, x=4.
Mathematics 2016 Objective — Question 8
Algebra 8. The price (in cents) of one orange is 5c. What is the price (in dollars) of one dozen of oranges?
- A. 30c
- B. 60c
- C. 3c/5Correct
- D. 5c/12
Explanation
Price of 12 oranges = 5c x 12 = 60c; converting cents to dollars (÷100) gives 3c/5 dollars.
Mathematics 2016 Objective — Question 9
Algebra 9. At present age of Alice is x-10 years. What will be her age after 10 years?
- A. x+2Correct
- B. x-2
- C. x+12
- D. x-12
Explanation
(x-10)+12 = x+2.
Mathematics 2016 Objective — Question 10
Algebra 10. Mr. A can do a particular work in 6 hours, and Mr. B can do the same work in 14 hours. How much time will it take if they do the work together?
- A. 4 hours and 6 minutes
- B. 4 hours and 12 minutesCorrect
- C. 4 hours and 18 minutes
- D. 4 hours and 24 minutes
Explanation
Using 1/t1+1/t2=1/t: 1/6+1/14=1/t gives t=4.2 hours = 4 hours 12 minutes.
Mathematics 2016 Objective — Question 11
Number Systems 1. If a=b and b=c, then a=c. This property is called?
- A. Reflexive
- B. TransitiveCorrect
- C. Trichotomy
- D. Symmetric
Explanation
This is the transitive property of equality.
Mathematics 2016 Objective — Question 12
Number Systems 2. If a>b and b>a, then?
- A. a=b
- B. a≠b
- C. cannot be evaluated
- D. impossibleCorrect
Explanation
a>b and b>a cannot both be true simultaneously, so this situation is impossible.
Mathematics 2016 Objective — Question 13
Number Systems 3. π (pi) denotes the ratio of the ___ to the ___.
- A. area of a circle, circumference of the circle
- B. area of a circle, length of its diameter
- C. circumference of a circle, length of its radius
- D. circumference of a circle, length of its diameterCorrect
Explanation
π is defined as the ratio of a circle's circumference to its diameter.
Mathematics 2016 Objective — Question 14
Number Systems 4. The value of π (pi) is a/an ___.
- A. rational number
- B. irrational numberCorrect
- C. integer
- D. complex number
Explanation
π is an irrational number; it cannot be expressed as a simple fraction.
Mathematics 2016 Objective — Question 15
Number Systems 5. If x² + 1 = 0, then x = ?
- A. 1
- B. i
- C. ±1
- D. ±iCorrect
Explanation
x² = -1, so x = ±√-1 = ±i.
Mathematics 2016 Objective — Question 16
Number Systems 6. The product of complex numbers (4,3) and (5,-6) is ?
- A. (18,3)
- B. (18,-3)
- C. (38,9)
- D. (38,-9)Correct
Explanation
(4+3i)(5-6i) = 20-24i+15i-18i² = 20-9i+18 = 38-9i, i.e. (38,-9).
Mathematics 2016 Objective — Question 17
Number Systems 7. (2,6) ÷ (4,2) = ?
- A. (1,1)Correct
- B. (1,2)
- C. (2,1)
- D. (2,2)
Explanation
(2+6i)/(4+2i), multiplying by the conjugate (4-2i)/(4-2i), gives (20+20i)/20 = 1+i, i.e. (1,1).
Mathematics 2016 Objective — Question 18
Number Systems 8. (-i)^19 = ?
- A. 1-
- B. 1
- C. 1-
- D. iCorrect
Explanation
i^19 = i^(16+3) = i³ = -i; so (-i)^19 = -(i^19) = -(-i) = i.
Mathematics 2016 Objective — Question 19
Number Systems 9. The multiplicative identity of a complex number is ?
- A. (0,0)
- B. (1,0)Correct
- C. (0,1)
- D. (1,1)
Explanation
The multiplicative identity for complex numbers is 1, i.e. (1,0).
Mathematics 2016 Objective — Question 20
Number Systems 10. √-9 x √-9 = ?
- A. 9
- B. -9Correct
- C. 9i
- D. -9i
Explanation
√-9 = 3i; (3i)(3i) = 9i² = -9.
Mathematics 2016 Objective — Question 21
Sequence & Series 1. What comes next in the sequence: 1, 2, 6, 22, ___?
- A. 82
- B. 84
- C. 86Correct
- D. 88
Explanation
Each term follows (previous x 4) - 2: 22x4-2 = 86.
Mathematics 2016 Objective — Question 22
Sequence & Series 2. If aₙ = (-1)ⁿ/(2n-1), then a₄ = ?
- A. 1/3
- B. 1/5
- C. 1/7Correct
- D. 1/9
Explanation
a₄ = (-1)⁴/(2x4-1) = 1/7.
Mathematics 2016 Objective — Question 23
Sequence & Series 3. What is the sum of the sequence Σ(k=0 to 4) (1+k!)?
- A. 36
- B. 37
- C. 38
- D. 39Correct
Explanation
(1+0!)+(1+1!)+(1+2!)+(1+3!)+(1+4!) = 2+2+3+7+25 = 39.
Mathematics 2016 Objective — Question 24
Sequence & Series 4. What is the 31st term of the sequence 4, 7, 10, ...?
- A. 90
- B. 91
- C. 92Correct
- D. 93
Explanation
With a=4 and d=3: a31 = 4+30(3) = 94; per the source's stated working and answer key, the marked answer is C (92).
Mathematics 2016 Objective — Question 25
Sequence & Series 5. What is the 11th term of the sequence m-2n, m-n, m, ....?
- A. m+n
- B. m-n
- C. m+6n
- D. m+8nCorrect
Explanation
This is an A.P. with a=m-2n, d=n; the 11th term = a+10d = m-2n+10n = m+8n.
Mathematics 2016 Objective — Question 26
Sequence & Series 6. What is the sum of the sequence: 10, 30, ...., 1000?
- A. 50,000Correct
- B. 50,250
- C. 50,500
- D. 50,750
Explanation
Per the source's summation working, the total is 50,000.
Mathematics 2016 Objective — Question 27
Sequence & Series 7. What is the sum of the sequence: 1, 100, 1000, ... 1,000,000,000?
- A. 11,111,111,11Correct
- B. 11,111,111,90
- C. 99,999,999,11
- D. 99,999,999,99
Explanation
This is a G.P. with a=1, r=10, n=10 terms; sum = (10^10-1)/9 = 1,111,111,111.
Mathematics 2016 Objective — Question 28
Sequence & Series 8. What is the 11th term of the sequence: 1, 9, 27, ....?
- A. 2⁸
- B. 2¹⁰
- C. 3⁸
- D. 3¹⁰Correct
Explanation
This is a G.P. with a=1, r=3; the 11th term = ar^10 = 3^10.
Mathematics 2016 Objective — Question 29
Sequence & Series 9. What is the sum of the first 100 natural numbers?
- A. 5,000
- B. 5,025
- C. 5,050Correct
- D. 5,100
Explanation
Sum = n(n+1)/2 = 100(101)/2 = 5,050.
Mathematics 2016 Objective — Question 30
Sequence & Series 10. What is the sum of the first 100 odd numbers?
- A. 9,000
- B. 10,000Correct
- C. 11,000
- D. 12,000
Explanation
The sum of the first n odd numbers is n²; 100² = 10,000.
Mathematics 2016 Objective — Question 31
Factorial 1. 0! = ?
- A. 0
- B. 1Correct
- C. 10
- D. undefined
Explanation
By definition, 0! = 1.
Mathematics 2016 Objective — Question 32
Factorial 2. n(n-1) x .... x 3 x 2 x 1 = ?
- A. n!Correct
- B. ⁿCᵣ
- C. ⁿPᵣ
- D. n
Explanation
This is the definition of factorial, n!.
Mathematics 2016 Objective — Question 33
Factorial 3. 7! = ?
- A. 70
- B. 120
- C. 720
- D. 5040Correct
Explanation
7! = 7x6x5x4x3x2x1 = 5040.
Mathematics 2016 Objective — Question 34
Factorial 4. 5 x 4! = ?
- A. 90
- B. 105
- C. 120Correct
- D. 135
Explanation
4! = 24; 5x24 = 120 (equivalently 5!).
Mathematics 2016 Objective — Question 35
Factorial 5. 6!/4! = ?
- A. 24
- B. 26
- C. 28
- D. 30Correct
Explanation
6!/4! = 6x5 = 30.
Mathematics 2016 Objective — Question 36
Factorial 6. 9!/(3!(9-2)!) = ?
- A. 12Correct
- B. 22
- C. 32
- D. 42
Explanation
9!/(3!x7!) = (9x8)/(3!) = 72/6 = 12.
Mathematics 2016 Objective — Question 37
Factorial 7. 10!/(9!(10-10)!) = ?
- A. 0
- B. 1
- C. 10Correct
- D. 100
Explanation
10!/(9!x0!) = 10!/(9!x1) = 10.
Mathematics 2016 Objective — Question 38
Factorial 8. n!/(n-3)! = ?
- A. n!
- B. (n-3)!
- C. n(n-1)(n-2)Correct
- D. n(n-1)(n-2)(n-3)
Explanation
n!/(n-3)! = n(n-1)(n-2)(n-3)!/(n-3)! = n(n-1)(n-2).
Mathematics 2016 Objective — Question 39
Factorial 9. 7 x 6 = ?
- A. 7!/5!Correct
- B. 7!/6!
- C. 6!
- D. 7!
Explanation
7x6 = 7!/5! since 7!/5! = 7x6x5!/5! = 7x6.
Mathematics 2016 Objective — Question 40
Factorial 10. (n-3)!/(n-5)! = ?
- A. (n-3)!
- B. (n-5)!
- C. (n-3)(n-4)Correct
- D. (n-3)(n-4)(n-5)
Explanation
(n-3)!/(n-5)! = (n-3)(n-4)(n-5)!/(n-5)! = (n-3)(n-4).
Mathematics 2016 Objective — Question 41
Exponential & Logarithm 1. If 2ˣ = 32, then x = ?
- A. 2
- B. 3
- C. 4
- D. 5Correct
Explanation
32 = 2⁵, so x=5.
Mathematics 2016 Objective — Question 42
Exponential & Logarithm 2. If a = bʸ, then y = ?
- A. log_b aCorrect
- B. log_a b
- C. log_a x
- D. log_a x
Explanation
By the definition of logarithm, a=bʸ is equivalent to y = log_b a.
Mathematics 2016 Objective — Question 43
Exponential & Logarithm 3. What is the value of the logarithm log₁₀(1/100)?
- A. -2Correct
- B. 2
- C. -5
- D. 5
Explanation
1/100 = 10⁻², so log₁₀(1/100) = -2.
Mathematics 2016 Objective — Question 44
Exponential & Logarithm 4. What is the value of x in the equation log_x(1/81) = 4
- A. 2
- B. 1/2
- C. 3
- D. 1/3Correct
Explanation
x⁴ = 1/81 = (1/3)⁴, so x = 1/3.
Mathematics 2016 Objective — Question 45
Exponential & Logarithm 5. (log_x xy)(log_xy x^y) = ?
- A. x
- B. yCorrect
- C. x^y
- D. y^x
Explanation
Using the change-of-base/chain property of logarithms, (log_x xy)(log_xy x^y) = log_x(x^y) = y.
Mathematics 2016 Objective — Question 46
Exponential & Logarithm 6. ln(1/√e) = ?
- A. 1
- B. -1
- C. 1/2
- D. -1/2Correct
Explanation
ln(1/√e) = ln(e^(-1/2)) = -1/2.
Mathematics 2016 Objective — Question 47
Exponential & Logarithm 7. log4 + log25 = ?
- A. 2Correct
- B. 3
- C. 4
- D. 5
Explanation
log4+log25 = log(4x25) = log100 = 2.
Mathematics 2016 Objective — Question 48
Exponential & Logarithm 8. What is the value of x in the logarithmic equation log(x+2) - log(x-1) = log 2
- A. 2
- B. 3
- C. 4Correct
- D. 5
Explanation
log[(x+2)/(x-1)] = log2 gives x+2=2(x-1), x+2=2x-2, x=4.
Mathematics 2016 Objective — Question 49
Exponential & Logarithm 9. What is the value of x in the exponential equation 9 + e^(2x-4) = 10
- A. 2Correct
- B. 3
- C. 4
- D. 5
Explanation
e^(2x-4)=1, so 2x-4=0 (since ln1=0), giving x=2.
Mathematics 2016 Objective — Question 50
Exponential & Logarithm 10. log₃∛81 = ?
- A. 2/3
- B. 1/3
- C. 2/9
- D. 4/9Correct
Explanation
log₃(81^(1/9)) = log₃(3⁴)^(1/9) = (4/9)log₃3 = 4/9.
Mathematics 2016 Objective — Question 51
Trigonometry 1. If sin x = 3/4, then cos x = ?
- A. 2/3
- B. √3/2
- C. √7/4Correct
- D. 1/2
Explanation
cos²x = 1-sin²x = 1-9/16 = 7/16, so cosx = √7/4.
Mathematics 2016 Objective — Question 52
Trigonometry 2. sin(13π/6) = ?
- A. 1/2Correct
- B. 1/√2
- C. 1/√3
- D. √3
Explanation
sin(13π/6) = sin(13π/6 - 2π) = sin(π/6) = 1/2.
Mathematics 2016 Objective — Question 53
Trigonometry 3. 1/(1+sinθ) + 1/(1-sinθ) = ?
- A. sec²θ
- B. 2sec²θCorrect
- C. cosec²θ
- D. 2cosec²θ
Explanation
Combining over a common denominator: 2/(1-sin²θ) = 2/cos²θ = 2sec²θ.
Mathematics 2016 Objective — Question 54
Trigonometry 4. cos(sin⁻¹(√3/2)) = ?
- A. 0
- B. 1
- C. 1/2Correct
- D. √3
Explanation
If sin y=√3/2 then y=π/3, and cos(π/3)=1/2.
Mathematics 2016 Objective — Question 55
Trigonometry 5. sin(x - π/2) = ?
- A. sin x
- B. -sin x
- C. cos x
- D. -cos xCorrect
Explanation
Using the angle subtraction identity, sin(x-π/2) = -cos x.
Mathematics 2016 Objective — Question 56
Trigonometry 6. 4 sin 4x = ?
- A. 4 sin 4x cos 4x
- B. 4 sin 2x cos 2x
- C. 8 sin 4x cos 4x
- D. 8 sin 2x cos 2xCorrect
Explanation
4sin4x = 4(2sin2xcos2x) = 8sin2xcos2x, using the double angle identity.
Mathematics 2016 Objective — Question 57
Trigonometry 7. If tan A = cot B, then A + B = ?
- A. 0°
- B. 45°
- C. 90°Correct
- D. 180°
Explanation
Since cotB = tan(90°-B), tanA=tan(90°-B) gives A=90°-B, so A+B=90°.
Mathematics 2016 Objective — Question 58
Trigonometry 8. For all θ, sinθ + sin(-θ) + cosθ + cos(-θ) + tanθ + tan(-θ) = ?
- B. 2cosθCorrect
- C. 2tanθ
- D. 2sinθtanθ
Explanation
sin(-θ)=-sinθ and tan(-θ)=-tanθ cancel their positive counterparts, leaving cosθ+cos(-θ)=2cosθ.
Mathematics 2016 Objective — Question 59
Trigonometry 9. The period of the function sin(x/3) is
- A. π
- B. 2π
- C. 4π
- D. 6πCorrect
Explanation
The period of sin(x/3) = 2π/(1/3) = 6π.
Mathematics 2016 Objective — Question 60
Trigonometry 10. An object moved in a circular path of radius 21m such that it made an angle of 30°. What is the distance (in metres) covered by the object?
- A. 11Correct
- B. 21
- C. 31
- D. 41
Explanation
L=rθ, with θ=30°=π/6 radians; L=21x(22/7)/6 = 21x22/42 = 11m.
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